Definition 6.3 ([1]}, Definition 7.3.1) 
Let \(\mathcal {C}\)  and \(\mathcal {D}\)  be two 2-categories. Let \(F,G: \mathcal {C} \rightarrow \mathcal {D}\)  be two functors and \(\alpha , \beta : F \Rightarrow G\)  be two natural transformations from \(F\)  to \(G\) . A modification \(\Gamma : \alpha \Rightarrow \beta \)  assigns to each object \(x\)  in \(\mathcal {C}\)  a 2-cell \(\Gamma _x: \alpha _x \rightarrow \beta _x\)  of \(\mathcal {D}\)  compatibly with the 2-cell components of \(F\)  and \(G\)  in the sense of equation
